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Concept

Figure-eight knot (mathematics)

Related publications (12)

Mechanics of Physical Knots: From Filaments in Contact to Surgical Suturing

Paul Johanns

In this thesis, we study the mechanics of tight physical knots. Knots are omnipresent in surgery, climbing, and sailing, with disastrous consequences when the filament or the rope fails to perform its function. Even if the importance of mechanical analysis ...

EPFL2023

The shapes of physical trefoil knots

Pedro Miguel Nunes Pereira de Almeida Reis, John Maddocks, Paul Johanns, Tomohiko Sano, Paul Grandgeorge

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly fle ...

2021

Experimenting with knots

Giovanni Dietler

Knots are interesting objects to experiment since their topological properties are combined with mechanical properties, fluid mechanics or dynamical properties like unknotting under the excitation of the thermal energy. Knots play also a role in biology be ...

SPRINGER HEIDELBERG2019

Periodic Motion of Sedimenting Flexible Knots

Giovanni Dietler, Krishnan Thyagarajan

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwi ...

APS2018

On chirality of toroidal embeddings of polyhedral graphs

Senja Dominique Barthel

We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a non-split link due to [2, 3]. Building on this and using the chirality of torus knots and ...

World Scientific Publishing2017

Sedimentation of macroscopic rigid knots and its relation to gel electrophoretic mobility of DNA knots

Giovanni Dietler, Cédric Weber

We address the general question of the extent to which the hydrodynamic behaviour of microscopic freely fluctuating objects can be reproduced by macrosopic rigid objects. In particular, we compare the sedimentation speeds of knotted DNA molecules undergoin ...

Nature Publishing Group2013

Ideal knots and other packing problems of tubes

This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...

EPFL2010

Computation and visualization of ideal knot shapes

We investigate numerical simulations and visualizations of the problem of tying a knot in a piece of rope. The goal is to use the least possible rope of a fixed, prescribed radius to tie a particular knot, e.g. a trefoil, a figure eight, and so on. The rop ...

EPFL2010

Scaling properties of DNA knots studied by atomic force microscopy

Erika Ercolini

The main subject of the present thesis is the experimental study of the scaling properties of DNA knots of different complexities by tapping mode atomic force microscopy (AFM) in air. Homo- or heterogeneous mixture of DNA knot types were deposited onto mic ...

EPFL2008

Fractal dimension and localization of DNA knots

Giovanni Dietler, Paolo De Los Rios, Guillaume Witz, Erika Ercolini

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the thr ...

American Physical Society2007

Simulations of electrophoretic collisions of DNA knots with gel obstacles

Giovanni Dietler, Paolo De Los Rios, Cédric Weber

Gel electrophoresis can be used to separate nicked circular DNA molecules of equal length but forming different knot types. At low electric fields, complex knots drift faster than simpler knots. However, at high electric field the opposite is the case and ...

Institute of Physics2006

Dynamic thread for real-time knot-tying

Real-time simulation of knot-tying with visual and force feedback is essential to VR surgery training. We present a physics-based simulator that enables realistic knot tying at haptic speed. The virtual thread obeys Newton's laws and behaves naturally. The ...

2005

Related publications (12)